There is no need to do "multi destination".

Just select GOI as your destination, and you will be presented with reasonably-priced itineraries with the last sector (from BOM or BLR) on Air India flights.

Beware that most airlines will refuse to interline bags across separate tickets.

Although it is technically possible in many cases, interlining is increasingly only done when a) the airlines are members of the same alliance [not the case here] and/or b) the travel was all booked on one ticket.

I have no experience of asking Emirates to interline on to a different ticket. However, you should be prudent and allow enough time between tickets just in case you are unlucky and/or outright refused having bags interline across 2 tickets.